iv.] DEDUCTIVE REASONING. 57 



PQ = PQB, (I) 



B = EC ; (2) 



hence, by substitution, as before, 



PQ = PQBO. (3) 



Except that the forniulse look a little more complicated 

 there is no difference whatever: 



The mood Ferio is of exactly the same character as 

 Darii or Barbara, except that it involves the use of a 

 negative term. Take the example, 



Bodies which are equally elastic in all directions do 



not doubly refract light ; 



Some crystals are bodies equally elastic in all direc- 

 tions; therefore, some crystals do not doubly 

 refract light. 



Assigning the letters as follows : 

 A = some crystals, 



B = bodies equally elastic in all directions, 

 C = doubly refracting light, 

 c = not doubly refracting light. 



Our argument is of the same form as before, and may 

 be concisely stated in one line, 



A = AB = ALc. 



If it is preferred to put PQ for the indefinite some crystals 

 we have 



PQ = PQB = PQBc. 



The only difference is that the negative term c takes the 

 place of C in the mood Darii. 



Ellipsis of Terms in Partial Identities. 



The reader will probably have noticed that the conclu- 

 sion which we obtain from premises is often more full than 

 that drawn by the old Aristotelian processes. Thus from 

 " Sodium is a metal," and " Metals conduct electricity," we 

 inferred (p. 55) that " Sodium = sodium, metal, conduct- 

 ing electricity," whereas the old logic simply concludes 

 that "Sodium conducts electricity." Symbolically, from 

 A = AB, and B - BC, we get A = ABC, whereas the old 

 logic gets at the most A = AC. It is therefore well to 

 show that without employing any other principles of 

 inference than those already described, we may infer 

 A = AC from A = ABC, though we cannot infer the latter 



